... I would spend the extra on a new frame
Who says that a new frame will not crack in the same place? We would all like to think it wouldn't, but you can't be certain.
The main thing to consider on this frame repair is what the parent metal is that the frame is made of. It may be chrome-moly or it might be just what is called mild steel. You could contact Daytec again to be sure. The welder will need to know what kind of filler rod to use and the material will determine if he needs to pre-heat or post-heat treat the weld.
I can’t see the pics from here at work but if the crack was at a weld, then it was probably caused by that weld not being done correctly in the first place and creating a weak point. It may have been undercut or not enough penetration. It may have been internal rust.
The way that Kapt. Describes is a foolproof way to repair any frame damage. But a good pipe welder can weld two hollow pipes together without anything on the inside and make the weld stronger than the surrounding pipe, they can even get a “bead” on the inside so that the outside can be ground flush, and still be stronger than the pipe. And you don’t need high frequency, all you need is a DC (direct current) machine. I’ve seen it done with an inverter welding machine (Miller Maxstar 150)) that was about as big as a lunchbox and plugs into a 110 outlet, and a gas bottle.